Personnel location tracking in areas where GPS signals are intermittent or unavailable has been an important consideration for military, firefighting, and consumer markets. Several researchers have reported on foot-borne micro-electromechanical sensors (MEMS) for personnel navigation. These sensors may include accelerometers, angular rate sensors, and magnetometers.
Schemes for navigation that include MEMS angular rate sensors have long been known that provide for correction of pitch and roll angular rate sensor bias error with accelerometers. Correction of yaw (compass heading) angular rate sensor bias error has not been possible just with accelerometers, as described in a paper by Eric Foxlin, “Pedestrian Tracking with Shoe-Mounted Inertial Sensors,” IEEE Computer Graphics and Applicatons, November/December, 2005, (“the Foxlin paper,”) incorporated herein by reference. While the author takes advantage of the zero-velocity state achieved with each foot fall to provide substantial navigation information, as the author states, “yaw (heading) and the yaw angular rate sensor bias are the only important extended Kalman filter states that aren't observable from zero-velocity measurements.” The Foxlin paper provides three solutions:                “using a much higher-performance angular rate sensor at least for the yaw axis which exhibits negligible drift over the time period . . . ;        providing heading-correcting measurements from a magnetic compass; or        providing position-correction measurements from GPS or other external aiding technologies.”        
A much higher-performance angular rate sensor is, of course, much more expensive, and GPS is often not available indoors and in outdoor locations between tall buildings. While a magnetic compass (magnetometers) has often been used as a reference to stabilize compass heading measurements, magnetometers have themselves been subject to error because of strong and unpredictable distortions of Earth's geomagnetic field, particularly in indoor environments.
Thus, a better system for reducing heading angular rate sensor bias error in personnel navigation and location tracking with MEMS and other low-cost sensors has been needed that does not rely on expensive angular rate sensors, GPS, or magnetometers. A better system has also been needed in attitude and heading reference systems (AHRS). Several embodiments of such a system are provided in this patent application.